A yarn that has been set has no torque

Every torque on the torsion ladder was computed the same way: a torsional rigidity times a twist rate, with the rigidity a constant and the twist whatever the spinner put in.

That describes a yarn for about the first few minutes of its life.

What setting is #

A yarn is set when it has been persuaded to accept its current shape as its natural one.

The mechanisms differ by fibre and the effect is the same. A cotton yarn conditioned at high humidity, or wetted and dried, relaxes: its cellulose chains rearrange under the internal stress until the stress is gone. A wool yarn steamed or autoclaved has its disulphide bonds broken and reformed in the new configuration. A thermoplastic yarn heated past its glass transition and cooled has its amorphous regions frozen where they now are.

In every case the yarn ends up with the same shape, the same twist, and no stress.

The distinction that matters #

Twist and torque are not the same thing, and a set yarn is where they come apart most completely.

Twist is a geometric quantity: how many times the material winds about the yarn’s own axis per unit length. A twist tester measures it by untwisting a length and counting, and it does not care whether the yarn is stressed.

Torque is a mechanical one: the moment the yarn exerts trying to unwind. It is the twist rate times a rigidity, and it exists only while the material is stressed.

A freshly spun yarn has both. A set yarn has the first and not the second.

So a specification saying “eight hundred turns a metre” says nothing about liveliness, and a specification saying “balanced” says nothing about twist. Two independent quantities, and the trade’s vocabulary conflates them.

What it does to the ladder #

Every result on the torsion ladder that involves a torque is a result about a fresh, unset yarn, and that is a narrower claim than any of them made.

The snarl threshold — 1.9 metres of the yarn’s own weight — is for a yarn straight off the spinning frame. A steamed yarn of the same twist needs no tension at all to stay straight, and that is why steaming is the trade’s answer to snarling.

The snarl radius — 1.6 millimetres — is likewise for an unset yarn, and a set one does not snarl to any radius.

The fold balance — where the two moments cancel — is a condition on moments, and a set yarn’s moments are nought at every fold ratio. The condition is vacuous.

Spirality — the residual torque that leans a jersey — is entirely a property of an unset yarn, and a jersey knitted from a set yarn does not lean.

Four of the ladder’s results, and all four are statements about a yarn in a condition it is in only briefly.

Which does not make them wrong #

It makes them conditional, which is different, and the condition is one the trade cares about a great deal.

A yarn is unset when it is being handled. Between the spinning frame and the loom or the machine, a yarn is wound, warped, sized, creeled and fed, and every one of those is a place where a lively yarn causes trouble. That is where snarling matters, and that is where the ladder’s results apply.

A yarn is usually set before it becomes fabric. Steaming after spinning, conditioning in the store, or the wetting a fabric gets in finishing: by the time the cloth is on a shelf, the yarn in it has mostly given its torque up.

So the ladder describes the yarn’s working life rather than its retirement, and that is the part of its life anybody is choosing a twist factor for.

Why setting is not permanent #

The uncomfortable half, and it is why “set” is a weaker word than it sounds.

A cotton yarn set by conditioning gives some of its torque back when it is wetted, because the mechanism was hydrogen bonds rearranging and water rearranges them again. That is why a cotton fabric that lay flat in the shop spirals after the first wash, and it is a complaint that has been made about cotton knitwear for as long as there has been any.

A wool yarn set by steaming holds better, because the mechanism is covalent, and holds less well than a wool set by a proper autoclave cycle.

A thermoplastic yarn heat-set above its eventual service temperature holds essentially permanently, and one set below it does not.

So setting is a partial and reversible removal of torque, and how partial depends on the fibre, the process and what happens afterwards. That is exactly the structure this collection has found for a set loop, where the fraction of natural curvature that setting has taken is a parameter the collection can bracket and not measure.

The parameter this collection cannot get at #

The honest position is that setting enters every torque result as a multiplier between nought and one, and nothing here can supply it.

Call it the set fraction: the proportion of a yarn’s original torque that survives. A fresh yarn is at one, a fully set yarn at nought, and everything in the trade is somewhere between.

Every torque on this ladder is multiplied by it. The snarl threshold goes as the square of it. The fold balance is unaffected in its position — it is where two moments cancel and both scale together — and completely affected in whether there is anything to balance.

This collection met the same parameter on the knitted ladder and found it cancels out of every balance the dimensions can be put into, so it cannot be measured from the fabric’s shape. Here it does not cancel: it multiplies a threshold, and a threshold is measurable.

So the snarl test is a measurement of the set fraction, and it may be the only direct one this collection has access to.

The measurement that would give it #

The test is the trade’s own liveliness test used as an instrument rather than as a specification.

Take a fresh yarn of known count and twist and measure the tension at which a slack loop snarls. The arithmetic predicts it from the twist and the stiffness ratio, at a set fraction of one.

Then steam it and measure again. The threshold falls by the square of whatever fraction of the torque survives, so a threshold that falls by a factor of four says the set fraction is a half.

That is a direct measurement of a quantity this collection has carried as an unknown for several ladders, it uses equipment every mill has, and nobody appears to have framed the liveliness test that way.

It also produces something more useful than a number: a curve of set fraction against steaming time, temperature and regain, which is what a finisher actually wants and which is currently arrived at by trial.

What it does to the fold rules #

One more consequence, and it resolves a tension left over from the folding rungs.

Those rungs found that the trade folds at a surface-angle condition rather than at a torque balance, and that a surface-balanced fold is left with about a tenth of its singles’ twist as residual — which is a real residual torque and would make a folded yarn slightly lively.

Folded yarns are slightly lively, and folded yarns are steamed. So the trade’s practice is: construct to the surface condition, then set away what is left.

That is a coherent and sensible way to make yarn, and it explains why nobody in the trade is troubled by the fact that the folding rule does not balance the torque. The folding is doing the geometry and the steaming is doing the mechanics, and each is doing the thing it is good at.

Why a set yarn is not a relaxed yarn #

Two words that get used interchangeably and should not, because the distinction decides what a process achieves.

Relaxation is a stress falling over time at a fixed shape. A yarn left on a bobbin loses torque over hours, and it does so by fibres creeping past one another. Nothing has changed about the fibres; they are in slightly different places.

Setting is a change in what the material considers its natural shape. The stress goes because there is no longer anything to be stressed about.

The two are distinguishable by what happens next. A relaxed yarn recovers some of its torque when it is disturbed, because the fibres have not moved far and friction is what is holding them. A set yarn does not, unless the setting mechanism is itself undone.

That is exactly the distinction this collection drew for a fabric’s dimensions, where relaxation is a fabric moving to wherever friction lets it stop and setting is something the material has done rather than something the friction has permitted.

So a mill’s practice of leaving yarn to condition and a mill’s practice of steaming it are not two ways of doing one thing. They produce different objects with different futures, and only the second survives a wash.

What was counted, and how #

Nothing on this rung is a new computation. Every number quoted is from the torsion ladder, restated with its condition attached.

What the rung adds is the multiplier and the observation that it multiplies a threshold rather than a value — which is what makes it measurable here and not measurable on the knitted ladder.

The claim that a set yarn has no torque at its own twist is not computed and is not this collection’s own: it is the definition of setting and it is what every steaming process is for.

What a finisher is actually choosing #

The set fraction is a process variable and it is worth saying what a finisher trades when they choose it, because the trade is not one-sided.

More setting means less liveliness, easier handling, a fabric that lies flat, and a knit that does not spiral. It also means a yarn that has given up some of the elastic recovery its twist was providing, and a fabric that is correspondingly less resilient.

Less setting keeps the recovery and the trouble together.

That is a real trade-off and it is the reason nobody sets everything as hard as possible. A wool yarn autoclaved until it has no torque at all makes a fabric that does not spiral and does not spring back either, and the resilience is what the wool was for.

So the set fraction is not a nuisance parameter to be driven to nought. It is a design variable with an optimum, and this collection has no way of computing where the optimum is — which is a fair statement of how much of finishing is outside its reach.

Where the model stops #

There is no model of setting here. The set fraction is named, its effect on each result is stated, and nothing predicts it from a temperature, a time or a regain.

And the rigidity may change too. Setting a yarn does not only remove its stress; it may also change how stiff it is, because rearranged chains are not the chains that were there. Nothing here separates a fall in torque from a fall in rigidity, and the snarl threshold depends on both — on the rigidity through the criterion and on the torque through the drive.

That is a real confound in the proposed measurement and it is worth stating: a threshold that falls after steaming could mean the torque went or the rigidity went, and separating them needs a second measurement, most obviously the coil radius, which depends on the ratio and not on the torque.

Nor is the timescale here. Torque relaxes over minutes, hours and months, so “set” and “unset” are the ends of a continuum in time as well as in process.

The one place the ladder’s results survive setting intact #

Not everything on the torsion ladder is a torque, and the results that are not survive completely.

The stiffness ratio is a material property. Setting does not change a fibre’s shear modulus or its tensile one to any interesting degree, so 2G/E is what it was.

The snarl radius is two over the ratio times the twist rate, and both survive: a set yarn does not snarl at all, and if it is made to snarl by twisting it further, the coil it takes is the same size.

The surface-angle folding rule is pure geometry — a diameter ratio and a helix angle — with no stress in it anywhere.

And every linking number and writhe is a count over an arrangement, and setting rearranges nothing.

So the ladder divides cleanly into results about a stressed yarn, which are conditional on the set fraction, and results about a shaped one, which are not. Four of each, near enough.

That division is worth carrying, because it is the same division this rung’s generalisation is about: a state variable decays and a geometric one does not, and a result inherits the lifetime of whichever it depends on.

The generalisation #

The rung is an instance of a habit worth having about any model that carries a material constant.

Ask how long the constant lasts.

A modulus is a property of a material and does not change. A stress is a property of a state and decays. This collection’s torsion ladder computes torques from a rigidity and a twist, and the twist is geometric and permanent while the stress it produces is neither.

That distinction is easy to lose because the two appear in the same product. Anything of the form “a constant times a state variable” inherits the state variable’s lifetime, and a result quoted without it is a result about a moment.

This collection has one other quantity with the same structure and has been careful about it: the crimp in a woven cloth is geometric and the contact force it produces is a stress, and the site’s own account of relaxation is precisely about how the second decays while the first does not.

What a specification would have to carry #

Putting the rung to use means saying what a yarn specification needs in order to describe liveliness, and it is not what specifications currently carry.

The twist, in turns per metre or as a twist factor, which is geometric and permanent and is already specified.

The setting treatment: what process, at what temperature, for how long, at what regain. That is a process description rather than a property and it is what actually decides the torque.

And the measured liveliness, by the hanging-loop test, on the yarn as it will be delivered rather than as it was spun.

The third is the one that matters and the one that is usually absent. A twist figure without it says what the yarn’s geometry is and nothing about what it will do on a creel.

That is the same complaint this collection has made about a fabric dimension quoted without its relaxation state: the number is correct, the quantity a user needs is a different one, and the specification names the first.

Who found it, and when #

Setting has been practised for as long as yarn has been made and understood mechanistically since the middle of the twentieth century, differently for each fibre class.

The distinction between a yarn’s twist and its torque is standard in the trade and is why the liveliness test exists as a separate measurement from the twist test.

What is this collection’s own is the observation that the snarl threshold is a measurement of the set fraction — a quantity the collection has carried as an unknown since it first tried to compute a knitted loop’s shape, and which it found could not be recovered from any fabric dimension.

Where the ladder goes next #

Setting removes a torque, and a fabric that has been through a wash gives some of it back. What a fabric does with a torque it has been given back is the next question, and it is one this collection can watch in an everyday object.

The twist a fabric gives back is what turns a T-shirt’s side seam round the body after the first wash.